To calculate the present value (PV) of an amount of money, given the future value (FV), interest rate, time period, and compounding frequency, we use the following formula:

$PV = \frac{FV}{(1 + \frac{r}{n})^{nt}}$

Where:

• $PV$ is the present value (what we want to find),
• $FV = 10,000$ is the future value,
• $r = 0.04$ is the annual interest rate (4%),
• $n = 2$ is the number of compounding periods per year (semiannually),
• $t = 3$ is the number of years.

Let's calculate the present value:

$PV = \frac{10,000}{(1 + \frac{0.04}{2})^{2 \times 3}}$

I will now compute this value.The present value (PV) of $10,000 to be received in 3 years, at an interest rate of 4% per year compounded semiannually, is $8,879.71.

Would you like further details on this calculation, or have any questions?

Here are some related questions to consider:

1. How does the frequency of compounding affect the present value?
2. What would the present value be if the interest rate increased to 5%?
3. How does continuous compounding differ from semiannual compounding in this scenario?
4. What happens to the present value if the time period is extended to 5 years?
5. How does inflation affect the real value of money over time?

Tip: The higher the frequency of compounding, the lower the present value will be for the same interest rate and future value.